Field of the Invention
The present invention concerns magnetic resonance imaging, and in particular a trajectory correction method and apparatus for k-space data in magnetic resonance imaging.
Description of the Prior Art
The term spatial frequency refers to variations in frequency per unit of distance in a certain direction of a periodically changing physical parameter. The spatial frequency k is a space vector, and is usually used for describing certain energies that spread in space in the form of waves (such as various electromagnetic waves). Due to the vector properties of k, usually three vector components kx, ky, and kz, which are mutually perpendicular to each other, are used to represent k. These three vector components kx, ky, and kz correspond to a three-dimensional coordinate system, and the mathematical space or domain corresponding to the coordinate system determined by kx, ky, and kz is called k-space.
In the field of magnetic resonance imaging, k-space is filled by magnetic resonance (MR) signal raw data with spatial orientation encoding information. Each MR image has k-space data corresponding thereto. Performing Fourier transform on the data in k-space decodes the spatial orientation encoding information in the raw data to obtain MR image data, i.e. mapping MR data with different signal intensities to corresponding spatial positions (i.e. allocating the signal intensity values to respective pixels of the MR image) can reconstruct an MR image. The data in k-space are very relevant to the MR image quality. Data in the central region of k-space determine the property (i.e. contrast ratio) of the MR image, while the edge (periphery) data of k-space determine the spatial resolution of the MR image.
Data acquisition sequences for acquiring MR data to enter into k-space include Cartesian sequences, non-Cartesian sequences, fast imaging sequences, etc. Compared to Cartesian sequences, non-Cartesian sequences and fast imaging sequences are very sensitive to gradient delay and eddy currents, that will result in a positional shift of the data points in k-space. If the shift between the actually obtained position of a data point and the desired filling trajectory of the data point is not corrected, then erroneous filling of k-space data will result, thus introducing image artifacts, and reducing the quality of the reconstructed MR image.
In the prior art, trajectory correction of data points in k-space is readily performed by calculating the desired trajectories of the data points of the entirety of k-space, which requires a significant amount of complicated calculations. Moreover, since the calculated region is the entirety of k-space, accumulated errors resulting from large region correction calculation are also very large, which affects the image quality.